# Stability of Curvature Measures

1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We address the problem of curvature estimation from sampled compact sets. The main contribution is a stability result: we show that the gaussian, mean or anisotropic curvature measures of the offset of a compact set K with positive $\mu$-reach can be estimated by the same curvature measures of the offset of a compact set K' close to K in the Hausdorff sense. We show how these curvature measures can be computed for finite unions of balls. The curvature measures of the offset of a compact set with positive $\mu$-reach can thus be approximated by the curvature measures of the offset of a point-cloud sample. These results can also be interpreted as a framework for an effective and robust notion of curvature.
Keywords :
Type de document :
Rapport
[Research Report] RR-6756, INRIA. 2008, pp.34
Domaine :

Littérature citée [32 références]

https://hal.inria.fr/inria-00344903
Contributeur : Frédéric Chazal <>
Soumis le : samedi 6 décembre 2008 - 15:17:52
Dernière modification le : vendredi 21 septembre 2018 - 15:38:03
Document(s) archivé(s) le : lundi 7 juin 2010 - 23:50:39

### Fichiers

RR-6756.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : inria-00344903, version 1
• ARXIV : 0812.1390

### Citation

Frédéric Chazal, David Cohen-Steiner, André Lieutier, Boris Thibert. Stability of Curvature Measures. [Research Report] RR-6756, INRIA. 2008, pp.34. 〈inria-00344903〉

### Métriques

Consultations de la notice

## 487

Téléchargements de fichiers